INTRODUCTION:
Computer chemistry has now become an increasingly useful tool for both industry and academia with the advent of increasingly sophisticated theoretical calculation methods and the computational resources more accessible1. Computer modeling of a molecule usually involves a graphical presentation of geometry or the configuration of the atoms of the molecule, followed by the application of a theoretical method2.
Molecular modeling is a general term that encompasses different techniques, molecular graphics, and computational chemistry to display, simulate, analyze, calculate and store the properties of molecules3.
The objective of this work is to develop a robust quantitative structure/ propriety relationship (QSPR) model that could predict toxicities for a set of phenols using theoretical molecular descriptors and to look for important characteristics related to toxicity values.
MATERIALS AND METHODS:
Dataset:
The experimental toxicity estimates for 81 phenols were derived from the literature4. Table 1 contains a complete list of the substances and their toxicities. Two subsets of the data set were chosen at random: a training set of 65 compounds and a test set of 16 compounds were chosen randomly from the data set. The training set was used to develop the genetic algorithm / multiple linear regressions (MLR), while the test set was used to assess the model's predictive capabilities.
Descriptors generation:
On a PC, we utilized the E-calc application to generate the Kier–Hall electron topological state (E– state) indices5, and then we used Hyperchem software to analyze the chemical structure of each compound6. The semi-empirical hold PM3 was used to obtain the final geometry. All calculations were done using non-configuration interaction at the restricted Hartree–Fock (RHF) level. The Polak-Ribiere algorithm was used to optimize the molecular structures, using a gradient norm limit of 0.001 kcal. A°-1.mol-1. The geometry data were entered into the Dragon software version 5.37, which generated 1600 descriptors of the Geometrical and GETAWAY types (Geometry, Topology, and Atoms Weighted AssemblY). Inside each group, descriptors with constant or near-constant values were removed. The descriptor with the highest pair correlation with the other descriptors was eliminated for each pair of associated descriptors (with correlation coefficient r≥0.95). Other ways of variable selection strategies have been deemed inferior to the GA (Genetic Algorithm)8. Therefore, in the MobyDigs version of Todeschini9, variable selection was done on the training set by maximizing the cross-validated explained variance Q2LOO.
Development and validation of the model:
The Ordinary Least Squares (OLS) approach was used to do multiple linear regression analysis using the MobyDigs program9.
The quality of the adjustment was evaluated by the coefficient of determination R2 and the mean square deviation calculated on the calibration set:
(1)
Cross-validation techniques have been applied for the evaluation of internal prediction (Q2LMO, bootstrap), model robustness (Q²LOO, Y-scrambling) and the mean quadratic prediction error (or SDEP):
(2)
Recalculating the model on (n-1) objects and using the resulting model to forecast the value of the discarded compound's dependent variable is what leave-one-out validation (LOO)10 is all about. For each of the n-objects, the procedure is repeated. The PRESS symbol (eq. (3)) denotes the sum of the squares of the prediction errors, which is used to define the prediction coefficient:
(3)
The root of the squared mean prediction error:
(4)
SCT is the total sum of squares; Denotes the response of the ith estimated object using a model obtained without involving this ith object and the mean value of the n observations; the summation is short on all the calibration compounds.
A value of Q² equal to 0.5 is considered satisfactory, and a value greater than 0.9 is excellent11,12.
In fact, if a high value of Q²LOO is a necessary condition for a possible high predictive capacity of a model, this condition alone is not sufficient13,14.To avoid overestimating the model's predictive capacity, the "leave-over-out" (LMO) procedure, repeated 8000 times, was also applied, excluding 50% of the objects at each stage (Q² LMO / 50). In the bootstrap validation technique, new samples of size (n) are simulated by random drawings with delivery. In this way, the calibration set, which retains its initial size (n), is generally made up of repeated objects, the set of tests gathering the excluded objects15,16.
The model is calculated on the calibration set and the predicted responses for the whole test. All squares of the differences between the predicted and observed values of the objects in the test set are collected in the PRESS. This procedure for constructing the calibration and evaluation sets is repeated several thousand times (8000 in this study), the PRESSs are summed, and an average prediction capacity is calculated17.
The application of the model, calculated on the calibration set, to the compounds of the external validation set makes it possible to reliably check the predictive capacity of the model obtained. Equation (5) allows the calculation of Q²EXT
(5)
The index (EXT) relating to the objects of the external validation set (or those of the evaluation set obtained by bootstrap), and the index (tr) to those of the calibration set).
With R², the SDEP parameter is also useful. It is calculated according to:
(6)
The sum of the objects of the validation set (EXT n).
The external Q²ext for the test set is determined by the following equation:
Q²ext = (7)
Other parameters are usable R2, which is determined for validation chemicals using the model created throughout training, and external standard deviation error prediction (SDEPext), which is described as follows:
(8)
Where the sum relates to the objects of the test set.
According to Golbraikh and Tropsha (14). A QSPR model has an acceptable prediction capability if it satisfies the following conditions:
Q²ext > 0.5 ; r² > 0.6
(r²-r²0)/ r² or (r²-r²’0)/ r² < 0.1
or 
Q²ext is the prediction coefficient for the test set; r is the correlation coefficient between the calculated and experimental values of the test set, r²0 and r'²0 are the coefficients of determination, r²0 (calculated as a function of the observed values) and r'²0 (observed values as a function of those calculated); K and K 'are the slopes of the regression lines passing through the origin, respectively of the calculated values as a function of those observed, and of the values observed as a function of those calculated.
QSAR DA (Application Domain):
The domain of application has been discussed using the Williams diagram (discussed in detail in11,12 representing the standardized prediction residuals as a function of the values of the levers hi.) Equation12 defines Lever of a compound in the original space of the independent variables (xi):
hi= xi (X T X)-1 xiT (i=1,…..,n) (12)
Where xi is the line vector of the compound i's descriptors, and X (n * p) is the model matrix determined from the values of the calibration set's descriptors; the index T designates the transposed vector (or matrix).
The lever's critical value (h *) is set to (3p + 1) / n. If hi < h*, the likelihood of agreement between the measured and projected values of compound I is the same as the calibration compounds. When compounds with hi> h* belong to the calibration set, they support the model, but they will have dubious projected values without necessarily being aberrant, as residues may be low.
RESULTS AND DISCUSSION:
The application of AG-VSS has led to several good models for prediction based on different sets of molecular descriptors. The best model with two explanatory variables was constructed using: (logkow)2; s-CH3, the values of these descriptors and the toxicities are summarized in Table 1.
The optimal model equation can be written as follows:
pCIC50 = - 0.0835 ± (0.07006) +0.112 ± (0.007408 (logkow)2 - 0.116 ± (0.01797) s-CH3
R² = 79.24; Q²LOO = 74.26; Q²BOOT = 72.12; Q²ext = 83.73; R²adj = 78.57; Kxx = 58.18;
Kxy= 53.96; F = 118.3193; S = 0.3296 in log unit.
Here: (logkow)2; s-CH3 are descriptors calculated successively with Hyperchem and E-calc software.
The R2 and R2 adj values indicate the quality of the adjustment; however, the small difference between R2 and Q2LOO demonstrates the model's resilience, which is also highly significant (high-value of Fisher's statistic F). The model's internal prediction capabilities and stability are both confirmed via bootstrap validation. The characteristics of this model can be evaluated using the statistical parameters listed in Table 2.
The value of t for a descriptor is related to its statistical significance. The high absolute values of t indicate that each regression coefficient is greater than the standard deviation associated with it.
The probability of t (p) for a descriptor gives its statistical significance when it is involved in a global QSPR model; it provides information on interactions between descriptors. Descriptors with probabilities of t less than 0.05 are considered statically significant for a given model, that is, their influence on the dependent variable is not random. The probability values of t for the two descriptors are all very much less than 0.05, indicating that they are very significant. The values of the variance inflation factor (FIV, all less than 5) and the correlation matrix reproduced in Table 4 suggest that these descriptors are weakly correlated with each other.
The statistical parameters of Tropsha et al12 were obtained for the test set, which of course satisfy the generally accepted condition and thus demonstrate the predictive power of the current model:
Tropsha et al12 statistical .'s parameters were produced for the test set, which, of course, satisfy the commonly accepted criteria and so verify the current model's predictive power:
Q²ext = 0.8287 > 0.5
r² = 0.8461 > 0. 6
T1 = (r²0-r²) / r² = -0.1711 < 0.1
With T2 = (r²-r²'0) / r² = - 0.1772 < 0.1
0.85≤ k = 0.9377 < 1.15 or 0.85 ≤ k '= 0.9509 ≤ 1.15
The correlation matrix in Table 3 indicates that these two descriptors are only weakly connected.
Figure.1 reproduces the values of the decimal logarithms of the predicted toxicities as a function of the decimal logarithms of the experimental toxicities, revealing a low dispersion characteristic of a good fit.
The results of the randomized models are compared with those of the initial real model using a graph representing the statistical parameters R² and Q². Figure 2 shows a clear separation between the statistics of the randomized responses and that of the initial model. This suggests that a structure- toxicity relationship has been established.
The Williams diagram (Figure 3) was used to define the scope of the MLR model. All compounds are in the range of ± 3σ so there are no aberrant points except the compounds named 3-Hydroxybenzylalcohol; (2,6-Diphenylphenol) ; 2,6-di(tert)butyl-4-methylphenol and all chemicals are hi <h * except the compounds named (2,6-Diphénylphenol; 2,6-Di(tert)butyl-4-methylphenol; 6-(tert)butyl-2,4-dimethylphenol).
Interpretation of results:
The first descriptor is n-octanol / water partition coefficient which is the ratio of the equilibrium concentration of a chemical substance in octanol to the concentration of the same substance in the water. It can be considered as a membrane that separates the interior and exterior of the living organism (Tetrahymena pyriformis).It is a factor of hydrophobicity; log's selection The importance of this parameter is supported by the fact that KOW is the most repeating descriptor in all bee models (with varying numbers of descriptors), making it the most essential descriptor among the specified descriptors17.
The second descriptor (S-CH3) is a Kier–Hall electron topological state (E–state) indices that defines the sums of each atom type's electropological state (E-state) value and or the counts of each atom type. The output can be in the form of a number of separate properties, one for each atom type, or a single property with a range of values.
ES count –S-CH3 denotes the number of atoms of the type S-CH3.